{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "<p align=\"center\">\n",
    "    <img src=\"https://github.com/GeostatsGuy/GeostatsPy/blob/master/TCG_color_logo.png?raw=true\" width=\"220\" height=\"240\" />\n",
    "\n",
    "</p>\n",
    "\n",
    "## Subsurface Data Analytics \n",
    "\n",
    "### Ridge Regression for Subsurface Data Analytics in Python \n",
    "\n",
    "\n",
    "#### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "\n",
    "##### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### PGE 383 Exercise: Ridge Regression for Subsurface Modeling in Python \n",
    "\n",
    "Here's a simple workflow, demonstration of ridge regression for subsurface modeling workflows. This should help you get started with building subsurface models with data analytics and machine learning. Here's some basic details about linear regression. \n",
    "\n",
    "Ridge regression is an extension of linear regresion, so let's review some basic details about linear regression first.  \n",
    "\n",
    "#### Linear Regression\n",
    "\n",
    "Linear regression for prediction.  Here are some key aspects of linear regression:\n",
    "\n",
    "**Parametric Model**\n",
    "\n",
    "* the fit model is a simple weighted linear additive model based on all the available features, $x_1,\\ldots,x_m$.\n",
    "\n",
    "* the parametric model takes the form of: \n",
    "\n",
    "\\begin{equation}\n",
    "y = \\sum_{\\alpha = 1}^m b_{\\alpha} x_{\\alpha} + b_0\n",
    "\\end{equation}\n",
    "\n",
    "**Least Squares**\n",
    "\n",
    "* least squares optimization is applied to select the model parameters, $b_1,\\ldots,b_m,b_0$ \n",
    "\n",
    "* we minize the error, residual sum of squares (RSS) over the training data: \n",
    "\n",
    "\\begin{equation}\n",
    "RSS = \\sum_{i=1}^n (y_i - (\\sum_{\\alpha = 1}^m b_{\\alpha} x_{\\alpha} + b_0))^2\n",
    "\\end{equation}\n",
    "\n",
    "* this could be simplified as the sum of square error over the training data, \n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{i=1}^n (\\Delta y_i)^2\n",
    "\\end{equation}\n",
    "\n",
    "**Assumptions**\n",
    "\n",
    "* **Error-free** - predictor variables are error free, not random variables \n",
    "* **Linearity** - response is linear combination of feature(s)\n",
    "* **Constant Variance** - error in response is constant over predictor(s) value\n",
    "* **Independence of Error** - error in response are uncorrelated with each other\n",
    "* **No multicollinearity** - none of the features are redundant with other features \n",
    "\n",
    "#### Other Resources\n",
    "\n",
    "This is a tutorial / demonstration of **Linear Regression**.  In $Python$, the $SciPy$ package, specifically the $Stats$ functions (https://docs.scipy.org/doc/scipy/reference/stats.html) provide excellent tools for efficient use of statistics.  \n",
    "I have previously provided this example in R and posted it on GitHub:\n",
    "\n",
    "1. R https://github.com/GeostatsGuy/geostatsr/blob/master/linear_regression_demo_v2.R\n",
    "2. Rmd with docs https://github.com/GeostatsGuy/geostatsr/blob/master/linear_regression_demo_v2.Rmd \n",
    "3. knit as an HTML document(https://github.com/GeostatsGuy/geostatsr/blob/master/linear_regression_demo_v2.html) \n",
    "\n",
    "#### Ridge Regression\n",
    "\n",
    "With ridge regression we add a hyperparameter, $\\lambda$, to our minimization, with a shrinkage penalty term.\n",
    "\n",
    "\\begin{equation}\n",
    "\\sum_{i=1}^n (y_i - (\\sum_{\\alpha = 1}^m b_{\\alpha} x_{\\alpha} + b_0))^2 + \\lambda \\sum_{j=1}^m b_{\\alpha}^2\n",
    "\\end{equation}\n",
    "\n",
    "As a result ridge regression has 2 criteria:\n",
    "\n",
    "* set the model parameters to minimize the error with training data\n",
    "\n",
    "* shrink the estimates of the slope parameters towards zero\n",
    "\n",
    "Note: the intercept is not affected by lambda.\n",
    "\n",
    "The $\\lambda$ is a hyperparameter that controls the degree of fit of the model and may be related to the model variance and bias trade-off.\n",
    "\n",
    "* for $\\lambda \\rightarrow 0$ the solution approaches linear regression, there is no bias (relative to a linear model fit), but the variance is high\n",
    "\n",
    "* as $\\lambda$ increases the model variance decreases and the model bias increases\n",
    "\n",
    "* for $\\lambda \\rightarrow \\infty$ the coefficients approach 0.0 and the model approaches the global mean\n",
    "\n",
    "#### Workflow Goals\n",
    "\n",
    "Learn the basics of ridge regression in Python to for analysis, modeling and prediction of porosity from density. This includes:\n",
    "\n",
    "* Basic Python workflows and data preparation\n",
    "\n",
    "* Training / fitting a ridge regression model\n",
    "\n",
    "* Checking the model and learning about the impact of hyperparameters\n",
    "\n",
    "#### Objective \n",
    "\n",
    "In the PGE 383: Stochastic Subsurface Modeling class I want to provide hands-on experience with building subsurface modeling workflows. Python provides an excellent vehicle to accomplish this. I have coded a package called GeostatsPy with GSLIB: Geostatistical Library (Deutsch and Journel, 1998) functionality that provides basic building blocks for building subsurface modeling workflows. \n",
    "\n",
    "The objective is to remove the hurdles of subsurface modeling workflow construction by providing building blocks and sufficient examples. This is not a coding class per se, but we need the ability to 'script' workflows working with numerical methods.    \n",
    "\n",
    "#### Getting Started\n",
    "\n",
    "Here's the steps to get setup in Python with the GeostatsPy package:\n",
    "\n",
    "1. Install Anaconda 3 on your machine (https://www.anaconda.com/download/). \n",
    "2. From Anaconda Navigator (within Anaconda3 group), go to the environment tab, click on base (root) green arrow and open a terminal. \n",
    "3. In the terminal type: pip install geostatspy. \n",
    "4. Open Jupyter and in the top block get started by copy and pasting the code block below from this Jupyter Notebook to start using the geostatspy functionality. \n",
    "\n",
    "There are examples below with these functions. You can go here to see a list of the available functions, https://git.io/fh4eX, other example workflows and source code. \n",
    "\n",
    "#### Import Required Packages\n",
    "\n",
    "Let's import the GeostatsPy package."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import os                                                   # to set current working directory \n",
    "import numpy as np                                          # arrays and matrix math\n",
    "import scipy.stats as st                                    # statistical methods\n",
    "import pandas as pd                                         # DataFrames\n",
    "import matplotlib.pyplot as plt                             # for plotting\n",
    "from sklearn.metrics import mean_squared_error, r2_score    # specific measures to check our models\n",
    "from sklearn.linear_model import Ridge                      # ridge regression implemented in scikit learn\n",
    "from sklearn.model_selection import cross_val_score         # multi-processor K-fold crossvalidation"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If you get a package import error, you may have to first install some of these packages. This can usually be accomplished by opening up a command window on Windows and then typing 'python -m pip install [package-name]'. More assistance is available with the respective package docs.  "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Set the working directory\n",
    "\n",
    "I always like to do this so I don't lose files and to simplify subsequent read and writes (avoid including the full address each time).  Also, in this case make sure to place the required (see below) data file in this working directory.  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#os.chdir(\"C:\\PGE337\")                                       # set the working directory"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Loading Data\n",
    "\n",
    "Let's load the provided dataset. 'Density_Por_data.csv' is available at https://github.com/GeostatsGuy/GeoDataSets. It is a comma delimited file with 20 density ($\\frac{g}{cm^3}$) and porosity (as a fraction) measures from the subsurface. We load the data file with the pandas 'read_csv' function into a data frame we called 'df' and then separate it into train and test datasets.  The smaples are in random order so we just split the dataset at the 80th sample.  We preview each with the head function from Pandas DataFrames."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Density</th>\n",
       "      <th>Porosity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1.281391</td>\n",
       "      <td>16.610982</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1.404932</td>\n",
       "      <td>13.668073</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>2.346926</td>\n",
       "      <td>9.590092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.348847</td>\n",
       "      <td>15.877907</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>2.331653</td>\n",
       "      <td>4.968240</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    Density   Porosity\n",
       "0  1.281391  16.610982\n",
       "1  1.404932  13.668073\n",
       "2  2.346926   9.590092\n",
       "3  1.348847  15.877907\n",
       "4  2.331653   4.968240"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "#df = pd.read_csv(\"Density_Por_data.csv\")                    # read a .csv file in as a DataFrame\n",
    "df = pd.read_csv(\"https://raw.githubusercontent.com/GeostatsGuy/GeoDataSets/master/Density_Por_data.csv\") # load from Prof. Pyrcz's GitHub\n",
    "df_train = df.iloc[0:80,:]                                  # extract a training set, note samples are random ordered\n",
    "df_train.head()                                             # preview the DataFrame"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Density</th>\n",
       "      <th>Porosity</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>80</th>\n",
       "      <td>1.750352</td>\n",
       "      <td>11.325941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>81</th>\n",
       "      <td>1.666285</td>\n",
       "      <td>15.609445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>82</th>\n",
       "      <td>1.466517</td>\n",
       "      <td>17.066529</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>83</th>\n",
       "      <td>1.650921</td>\n",
       "      <td>13.876841</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>84</th>\n",
       "      <td>0.996736</td>\n",
       "      <td>20.964941</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "     Density   Porosity\n",
       "80  1.750352  11.325941\n",
       "81  1.666285  15.609445\n",
       "82  1.466517  17.066529\n",
       "83  1.650921  13.876841\n",
       "84  0.996736  20.964941"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test = df.iloc[80:]                                      # extract a testing set, note samples are random ordered\n",
    "df_test.head()                                              # preview the DataFrame"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is useful to review the summary statistics of our loaded DataFrame.  That can be accomplished with the 'describe' DataFrame member function.  We transpose to switch the axes for ease of visualization.  We will summarize over the training and testing subsets separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Density</th>\n",
       "      <td>80.0</td>\n",
       "      <td>1.759945</td>\n",
       "      <td>0.295260</td>\n",
       "      <td>1.067960</td>\n",
       "      <td>1.552707</td>\n",
       "      <td>1.767908</td>\n",
       "      <td>1.953262</td>\n",
       "      <td>2.410560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Porosity</th>\n",
       "      <td>80.0</td>\n",
       "      <td>12.187127</td>\n",
       "      <td>3.125755</td>\n",
       "      <td>4.966421</td>\n",
       "      <td>10.011526</td>\n",
       "      <td>12.170687</td>\n",
       "      <td>14.063670</td>\n",
       "      <td>19.600717</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          count       mean       std       min        25%        50%  \\\n",
       "Density    80.0   1.759945  0.295260  1.067960   1.552707   1.767908   \n",
       "Porosity   80.0  12.187127  3.125755  4.966421  10.011526  12.170687   \n",
       "\n",
       "                75%        max  \n",
       "Density    1.953262   2.410560  \n",
       "Porosity  14.063670  19.600717  "
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_train.describe().transpose()   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>count</th>\n",
       "      <th>mean</th>\n",
       "      <th>std</th>\n",
       "      <th>min</th>\n",
       "      <th>25%</th>\n",
       "      <th>50%</th>\n",
       "      <th>75%</th>\n",
       "      <th>max</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Density</th>\n",
       "      <td>25.0</td>\n",
       "      <td>1.667429</td>\n",
       "      <td>0.257608</td>\n",
       "      <td>0.996736</td>\n",
       "      <td>1.568988</td>\n",
       "      <td>1.718085</td>\n",
       "      <td>1.791432</td>\n",
       "      <td>2.339324</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Porosity</th>\n",
       "      <td>25.0</td>\n",
       "      <td>13.632564</td>\n",
       "      <td>2.948887</td>\n",
       "      <td>9.489298</td>\n",
       "      <td>11.325941</td>\n",
       "      <td>13.767060</td>\n",
       "      <td>15.051759</td>\n",
       "      <td>20.964941</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "          count       mean       std       min        25%        50%  \\\n",
       "Density    25.0   1.667429  0.257608  0.996736   1.568988   1.718085   \n",
       "Porosity   25.0  13.632564  2.948887  9.489298  11.325941  13.767060   \n",
       "\n",
       "                75%        max  \n",
       "Density    1.791432   2.339324  \n",
       "Porosity  15.051759  20.964941  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_test.describe().transpose()   "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we extract the ndarrays with porsity and density, training and testing datasets separate arrays for convenience."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "por_train = df_train['Porosity'].values                     # make a shallow copy of the features for convenvience\n",
    "df = pd.read_csv(\"Density_Por_data.csv\")                    \n",
    "den_train = df_train['Density'].values\n",
    "por_test = df_test['Porosity'].values\n",
    "den_test = df_test['Density'].values\n",
    "n_train = len(df_train); n_test = len(df_test)              # get the number of data in training and testing"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's look at the training and testing data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(111)\n",
    "plt.scatter(df_train[\"Density\"].values, df_train[\"Porosity\"],  color='black', s = 20, alpha = 0.3, label = 'training')\n",
    "plt.scatter(df_test[\"Density\"].values, df_test[\"Porosity\"],  color='red', s = 20, alpha = 0.3, label = 'testing')\n",
    "plt.title('Linear Regression Porosity from Density with Training Data'); plt.xlabel('Density (g/cm^3)'); plt.ylabel('Porosity (%)')\n",
    "plt.legend()\n",
    "plt.xlim(1.,2.6)#; plt.ylim(0,1500000)\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.0, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Linear Regression Model\n",
    "\n",
    "Let's first calculate the linear regression model. We use scikit learn and then extend the same workflow to ridge regression."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  -8.961, Intercept:  27.958\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from sklearn import linear_model\n",
    "\n",
    "# Step 1. Instantiate the Model \n",
    "linear_reg = linear_model.LinearRegression()\n",
    "\n",
    "# Step 2: Fit the Data on Training Data\n",
    "linear_reg.fit(df_train[\"Density\"].values.reshape(n_train,1), df_train[\"Porosity\"]) # fit model\n",
    "density_model = np.linspace(1.2,2.4,10)\n",
    "\n",
    "# Print the model parameters\n",
    "porosity_model = linear_reg.predict(density_model.reshape(10,1)) # predict with the fit model\n",
    "print('Coefficients: ', str(round(linear_reg.coef_[0],3)) + ', Intercept: ', str(round(linear_reg.intercept_,3))) \n",
    "\n",
    "# Plot model fit\n",
    "plt.subplot(111)\n",
    "plt.scatter(df_train[\"Density\"].values, df_train[\"Porosity\"],  color='black', s = 20, alpha = 0.3)\n",
    "plt.plot(density_model,porosity_model, color='red', linewidth=1)\n",
    "plt.title('Linear Regression Porosity from Density with Training Data'); plt.xlabel('Density (g/cm^3)'); plt.ylabel('Porosity (%)')\n",
    "plt.xlim(1.,2.6)#; plt.ylim(0,1500000)\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=1.0, top=1.0, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's run some quick model checks.  Much more could be done, but I limit this for breviety here. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance explained: 0.58\n",
      "Residual: mean = -0.62, standard deviation = 3.13\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Step 3: - Make predictions using the testing dataset\n",
    "y_pred = linear_reg.predict(df_test['Density'].values.reshape(n_test,1))\n",
    "\n",
    "# Report the goodness of fit\n",
    "print('Variance explained: %.2f' % r2_score(df_test['Porosity'].values, y_pred))\n",
    "\n",
    "# Plot testing diagnostics \n",
    "plt.subplot(121)\n",
    "plt.scatter(df_test['Density'].values, df_test['Porosity'].values,  color='black', s = 20, alpha = 0.3)\n",
    "plt.scatter(df_test['Density'], y_pred, color='blue', s = 20, alpha = 0.3)\n",
    "plt.title('Linear Regression Model Testing - Production from Porosity'); plt.xlabel('Density (g/cm^3)'); plt.ylabel('Porosity (%)')\n",
    "plt.xlim(1.0,2.6); plt.ylim(5,24)\n",
    "\n",
    "y_res = y_pred - df_test['Porosity'].values\n",
    "\n",
    "print('Residual: mean = ' + str(round(np.average(y_res),2)) + ', standard deviation = ' + str(round(np.var(y_res),2)))\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.hist(y_res, alpha = 0.2, color = 'red', edgecolor = 'black', bins=20)\n",
    "plt.title('Linear Regression Model Prediction Error - Porosity form Density'); plt.xlabel('Porosity Estimation Error (%) (Estimate - Truth)'); plt.ylabel('Frequency')\n",
    "plt.xlim(-4,4)#; plt.ylim(0,1500000)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.2, top=1.2, wspace=0.3, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Ridge Regression\n",
    "\n",
    "Let's replace the scikit learn linear regression method with the scikit learn ridge regression method.  Note, we must now set the lambda hyperparameter.\n",
    "\n",
    "* the hyperparameter is set with the instantiation of the model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Coefficients:  -8.961, Intercept:  27.958\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "lam = 1.0\n",
    "\n",
    "# Step 1. Instantiate the Model \n",
    "ridge_reg = Ridge(alpha=lam)\n",
    "\n",
    "# Step 2: Fit the Data on Training Data\n",
    "ridge_reg.fit(df_train[\"Density\"].values.reshape(n_train,1), df_train[\"Porosity\"]) # fit model\n",
    "density_model = np.linspace(1.2,2.4,10)\n",
    "\n",
    "# Print the model parameters\n",
    "porosity_model = ridge_reg.predict(density_model.reshape(10,1)) # predict with the fit model\n",
    "print('Coefficients: ', str(round(linear_reg.coef_[0],3)) + ', Intercept: ', str(round(linear_reg.intercept_,3))) \n",
    "\n",
    "# Plot model fit\n",
    "plt.subplot(111)\n",
    "plt.scatter(df_train[\"Density\"].values, df_train[\"Porosity\"],  color='black', s = 20, alpha = 0.3)\n",
    "plt.plot(density_model,porosity_model, color='red', linewidth=1)\n",
    "plt.title('Ridge Regression Porosity from Density with Training Data'); plt.xlabel('Density (g/cm^3)'); plt.ylabel('Porosity (%)')\n",
    "plt.xlim(1.,2.6); plt.ylim(8,17)\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.0, wspace=0.2, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's repeat the simple model checks that we applied with our linear regression model."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance explained: 0.55\n",
      "Residual: mean = -0.72, standard deviation = 3.22\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Step 3: - Make predictions using the testing dataset\n",
    "y_pred = ridge_reg.predict(df_test['Density'].values.reshape(n_test,1))\n",
    "\n",
    "# Report the goodness of fit\n",
    "print('Variance explained: %.2f' % r2_score(df_test['Porosity'].values, y_pred))\n",
    "\n",
    "# Plot testing diagnostics \n",
    "plt.subplot(121)\n",
    "plt.scatter(df_test['Density'].values, df_test['Porosity'].values,  color='black', s = 20, alpha = 0.3)\n",
    "plt.scatter(df_test['Density'], y_pred, color='blue', s = 20, alpha = 0.3)\n",
    "plt.title('Linear Regression Model Testing - Production from Porosity'); plt.xlabel('Density (g/cm^3)'); plt.ylabel('Porosity (%)')\n",
    "plt.xlim(1.0,2.6); plt.ylim(5,24)\n",
    "\n",
    "y_res = y_pred - df_test['Porosity'].values\n",
    "\n",
    "print('Residual: mean = ' + str(round(np.average(y_res),2)) + ', standard deviation = ' + str(round(np.var(y_res),2)))\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.hist(y_res, alpha = 0.2, color = 'red', edgecolor = 'black', bins=20)\n",
    "plt.title('Linear Regression Model Prediction Error - Porosity form Density'); plt.xlabel('Porosity Estimation Error (%) (Estimate - Truth)'); plt.ylabel('Frequency')\n",
    "plt.xlim(-4,4)#; plt.ylim(0,1500000)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.2, top=1.2, wspace=0.3, hspace=0.2)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Interesting, we explained less variance and have a larger residual standard deviation (more error).\n",
    "\n",
    "* we see we actually reduced both testing variance explained and accuracy \n",
    "\n",
    "#### Investigating the Lambda Hyperparameter\n",
    "\n",
    "Let's loop over multiple lambda values - from 0 to 100 and observe the change in:\n",
    "\n",
    "* training and testing, mean square error (MSE) and variance explained"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 8 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Arrays to store the results\n",
    "ncases = 100\n",
    "lamd_mat = np.linspace(0.0,100.0,ncases)\n",
    "density_model = np.linspace(1.2,2.4,10)\n",
    "var_explained_train = np.zeros(ncases); var_explained_test = np.zeros(ncases)\n",
    "mse_train = np.zeros(ncases); mse_test = np.zeros(ncases)\n",
    "\n",
    "for ilam in range(0,len(lamd_mat)):                         # Loop over all lambda values\n",
    "    ridge_reg = Ridge(alpha=lamd_mat[ilam])\n",
    "    ridge_reg.fit(df_train[\"Density\"].values.reshape(n_train,1), df_train[\"Porosity\"]) # fit model\n",
    "\n",
    "    porosity_model = ridge_reg.predict(density_model.reshape(10,1)) # predict with the fit model  \n",
    "    porosity_pred_train = ridge_reg.predict(df_train['Density'].values.reshape(n_train,1)) # predict with the fit model   \n",
    "    var_explained_train[ilam] = r2_score(df_train['Porosity'].values, porosity_pred_train)\n",
    "    mse_train[ilam] = mean_squared_error(df_train['Porosity'].values, porosity_pred_train) \n",
    "    \n",
    "    porosity_pred_test = ridge_reg.predict(df_test['Density'].values.reshape(n_test,1))\n",
    "    var_explained_test[ilam] = r2_score(df_test['Porosity'].values, porosity_pred_test)\n",
    "    mse_test[ilam] = mean_squared_error(df_test['Porosity'].values, porosity_pred_test)    \n",
    "   \n",
    "    if ilam <= 7:\n",
    "        plt.subplot(4,2,ilam+1)\n",
    "        plt.scatter(df_train[\"Density\"].values, df_train[\"Porosity\"],  color='black', s = 20, alpha = 0.3)\n",
    "        plt.plot(density_model,porosity_model, color='red', linewidth=1)\n",
    "        plt.title('Ridge Regression Porosity from Density with Training Data - Lambda = ' + str(round(lamd_mat[ilam],2))); plt.xlabel('Density (g/cm^3)'); plt.ylabel('Porosity (%)')\n",
    "        plt.xlim(1.,2.6); plt.ylim(5,24)\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=4.2, wspace=0.2, hspace=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can observed from the first 8 cases above of ridge regression model fit that increase in the lambda hyper parameter decreases the slope of the linear fit.\n",
    "\n",
    "Let's plot the MSE and variance explained over training and testing datasets."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 2 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.subplot(121)\n",
    "plt.plot(lamd_mat, var_explained_train,  color='blue', linewidth = 2, label = 'Training')\n",
    "plt.plot(lamd_mat, var_explained_test,  color='red', linewidth = 2, label = 'Test')\n",
    "plt.title('Variance Explained vs. Lambda'); plt.xlabel('Lambda'); plt.ylabel('Variance Explained')\n",
    "plt.xlim(0.,100.); plt.ylim(0,1.0)\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.0, wspace=0.2, hspace=0.2)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplot(122)\n",
    "plt.plot(lamd_mat, mse_train,  color='blue', linewidth = 2, label = 'Training')\n",
    "plt.plot(lamd_mat, mse_test,  color='red', linewidth = 2, label = 'Test')\n",
    "plt.title('MSE vs. Lambda'); plt.xlabel('Lambda'); plt.ylabel('Mean Square Error')\n",
    "plt.xlim(0.,100.); plt.ylim(0,10.0)\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.0, wspace=0.2, hspace=0.2)\n",
    "plt.legend()\n",
    "\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.2, wspace=0.2, hspace=0.3)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We observe that as we increase the lambda parameter the variance explained decreases and the mean square error increases.\n",
    "\n",
    "* this makes sense as the data has a consistent linear trend and as the slope 'shrinks' to zero the error increases and the variance explained decreases\n",
    "\n",
    "* there could be other cases where the reduced slope actually performs better in testing.  For example with sparce and noisy data. \n",
    "\n",
    "#### Model Variance \n",
    "\n",
    "Now let's explore the concept of model variance, an important part of machine learning accuracy in testing. \n",
    "\n",
    "* the sensitivity of the model to the specfic training data\n",
    "\n",
    "* as lambda increases the sensitivity to the training data, model variance decreases\n",
    "\n",
    "Let's demonstrate this with this workflow:\n",
    "\n",
    "* loop over multiple lambda values\n",
    "    * loop over multiple bootstrap samples of the data\n",
    "        * calculate the ridge regression fit (slope)\n",
    "    * calculate the variance of these bootstrap results\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "L = 200                                                     # the number of bootstrap realizations \n",
    "nsamples = 20                                               # the number of samples in each bootstrap realization\n",
    "nlambda = 100                                               # number of lambda values to evaluate\n",
    "\n",
    "coef_mat = np.zeros(L)                                      # declare arrays to store the results\n",
    "variance_coef = np.zeros(nlambda)\n",
    "\n",
    "lamd_mat = np.linspace(0.0,100.0,nlambda)\n",
    "df = pd.read_csv(\"Density_Por_data.csv\")                    \n",
    "for ilam in range(0,len(lamd_mat)):                         # loop over all lambda values                   \n",
    "    for l in range(0, L):                                   # loop over all bootstrap realizations\n",
    "        df_sample = df.sample(n = nsamples)                 # random sample (1 bootstrap)\n",
    "        ridge_reg = Ridge(alpha=lamd_mat[ilam])             # instatiate model\n",
    "        ridge_reg.fit(df_sample[\"Density\"].values.reshape(nsamples,1), df_sample[\"Porosity\"]) # fit model\n",
    "        coef_mat[l] = ridge_reg.coef_[0]                    # get the slope parameter\n",
    "    \n",
    "    variance_coef[ilam] = np.var(coef_mat)                  # calculate the variance of the slopes over the L bootstraps"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's plot the result."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x2018e3266c8>"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SAIwcOTJF15L4nBEjRpz2+Msuu4w5c+awbt06AHbu3AlAixYtePXVVxPC+JIlS1LUf3rIVqFUEx2JiIiIiMjp7N+/ny5dulCtWjVq1arFTz/9dNyoJECpUqV47rnnaNq0KbVr16Zu3brccMMNQGjU8scff+SSSy7hyy+/pG/fvgCMGTOGd999l9q1a1O9evWTThZUuHBhGjZsSMmSJY+7Rbd///60a9eORo0acc4556ToWh577DGeeOIJ/va3vxEXF3fa44sXL87QoUNp27YttWvXTrgNuU+fPsTGxlKrVi1q1KhBnz59UtR/erCghssjqV69eh6ptYVEREREROTMrFy5MkOeVYyU/Pnzs3///qDLCERyPzsz+87d07xGTbYaKRUREREREZGsRaFUREREREQkFc7WUdJIUSgVERERERGRwGSrUKqJjkREREREsobsOLdNdhepn1m2CqXuPt3dux5bIFZERERERDKfPHnysGPHDgXTLMTd2bFjB3ny5En3tqPTvUUREREREZFTKFOmDJs2bWLbtm1BlyKpkCdPHsqUKZPu7SqUioiIiIhIhsqZM+dx63PK2S1b3b4rIiIiIiIiWYtCqYiIiIiIiARGoVREREREREQCk61CqZaEERERERERyVqyVSjVkjAiIiIiIiJZS7YKpSIiIiIiIpK1KJSKiIiIiIhIYBRKRUREREREJDAKpSIiIiIiIhIYhVIREREREREJjEKpiIiIiIiIBEahVERERERERAKTrUKpmbU2s6F79uwJuhQRERERERFJgWwVSt19urt3LVSoUNCliIiIiIiISApkq1AqIiIiIiIiWYtCqYiIiIiIiARGoVREREREREQCo1AqIiIiIiIigVEoFRERERERkcAolIqIiIiIiEhgFEpFREREREQkMAqlIiIiIiIiEhiFUhEREREREQmMQqmIiIiIiIgEJluG0r/++ivoEkRERERERCQFooMuID2ZWWugdUxMTNCliIiIiIiISApkq5FSd5/u7l0PHTrE7Nmzgy5HRERERERETiNbhdLEnnjiCdw96DJERERERETkFLJlKI2Ojmb+/PlMnz496FJERERERETkFLJlKC1VqhQATz75JHFxcQFXIyIiIiIiIieTLUNp8eLFOf/881mxYgXjxo0LuhwRERERERE5iWwZSs2M/v37A9C3b1+OHDkSbEEiIiIiIiKSrGwZSgE6d+5MlSpVWLduHe+8807Q5YiIiIiIiEgysm0ojY6OZuDAgQA888wzHDhwIOCKREREREREJKlsG0oB2rZtS7169fjjjz949dVXgy5HREREREREksjWodTMePbZZwEYPHgwu3btCrgiERERERERSSxbh1KAZs2a0bRpU3bv3s2///3voMsRERERERGRRLJ9KE08WjpkyBC2bNkScEUiIiIiIiJyTLYPpQANGzbkhhtu4NChQwmTH4mIiIiIiEjwzopQCjBo0CDMjKFDh7J27dqgyxERERERERHOolBavXp1OnfuzNGjR+nXr1/Q5YiIiIiIiAhnUSgFGDBgADlz5mTMmDEsX7486HJERERERETOemdVKC1Xrhz33nsv7s4jjzyCuwddkoiIiIiIyFkt04dSM8tnZiPN7G0zu/VM2+vbty+FChVi1qxZTJ8+PT1KFBERERERkTQKJJSa2TAz22pmK5Jsv9bMVpnZGjN7PLy5LTDZ3e8Brj/TvosXL86AAQMAePjhhzl8+PCZNikiIiIiIiJpFNRI6Qjg2sQbzCwKeB1oCVQDOplZNaAM8Fv4sLj06Pyf//wn1apVY+3atbz88svp0aSIiIiIiIikQSCh1N2/BnYm2VwfWOPua939CDAeuAHYRCiYQjrVmzNnToYMGQKElorZvHlzejQrIiIiIiIiqZSZniktzf8fEYVQGC0NfADcZGZvAid9CNTMuprZYjNbvG3bttN21qxZM2688UYOHDjA448/ftrjRUREREREJP1lplBqyWxzdz/g7ne6+33uPuZkJ7v7UHev5+71ihcvnqIOX3rpJXLnzs3o0aP59ttv01q3iIiIiIiIpFFmCqWbgLKJPpcBfo9kh+XLl+eRRx4BoHv37sTFpcsjqyIiIiIiIpJCmSmULgIqmVl5M8sFdASmpaYBM2ttZkP37NmT4nOeeOIJSpcuzXfffcfw4cNTV7GIiIiIiIickaCWhBkHzAMqm9kmM7vb3Y8CDwCfAiuBie7+Y2radffp7t61UKFCKT4nX758vPDCCwD861//Yvfu3anpUkRERERERM5AULPvdnL3Uu6e093LuPu74e0fu/tF7n6huw/KqHo6duzIFVdcwbZt23j66aczqlsREREREZGzXma6fTcwZsYrr7yCmfHqq6+ycuXKoEsSERERERE5K2SrUJqWZ0qPqVOnDvfccw9Hjx6lR48euHsEKhQREREREZHEslUoTcszpYkNHDiQwoULM2vWLKZNS9UcSyIiIiIiIpIG2SqUnqnixYszYMAAAHr27Mnhw4cDrkhERERERCR7UyhN4r777qN69eqsXbuWhx56KOhyREREREREsrVsFUrP5JnSY3LmzMl7771H7ty5GTp0KCNGjEi/AkVEREREROQ42SqUnukzpcfUrVuX119/HQiNnC5dujQ9yhMREREREZEkslUoTU933303d999N4cPH+amm25i9+7dQZckIiIiIiKS7SiUnsKrr75KnTp1WLt2Lbfffjvx8fFBlyQiIiIiIpKtKJSeQkxMDO+//z6FCxdm+vTpDB48OOiSREREREREspVsFUrTY6KjpMqXL8/o0aMBeOqpp/jiiy/SrW0REREREZGzXbYKpek10VFS1113HX369CE+Pp6OHTuyadOmdG1fRERERETkbJWtQmkk9evXj+bNm7N9+3batWvHkSNHgi5JREREREQky1MoTaGoqCjGjBlD2bJlmT9/Pr169Qq6JBERERERkSxPoTQVzjnnHCZPnkyuXLl47bXXGDZsGO4edFkiIiIiIiJZVrYKpZGY6Cip+vXrM2TIECC0lmnFihV58sknWb58uQKqiIiIiIhIKll2DFL16tXzxYsXR6x9d2fw4MG88sorbNmyJWF7tWrV6NixIx07dqRSpUoR619ERERERCSzMLPv3L1ems9XKE27uLg45s6dy/jx45k8eTI7duxI2HfJJZfQsWNH/vGPf1C4cOGI1yIiIiIiIhIEhdJkZFQoTSw2NpYvvviCcePGMWXKFPbt2wdA7dq1mTdvHjExMRlaj4iIiIiISEY401CarZ4pDVLOnDm59tprGTlyJFu3buWDDz6gQoUKLFu2jIceeijo8kRERERERDIlhdIIyJMnDzfeeCPvv/8+uXPn5u2332bUqFFBlyUiIiIiIpLppCiUmtkFZtYs/D7GzApEtqzs4eKLL+a1114DoFu3bvz4448BVyQiIiIiIpK5nDaUmtk9wGTgrfCmMsCHkSwqrTJiSZjUuvvuu+ncuTMHDx6kXbt27N+/P+iSREREREREMo2UjJTeD/wN2Avg7quBEpEsKq3cfbq7dy1UqFDQpSQwM958802qVavGypUr6datm9YzFRERERERCUtJKP3L3Y8c+2Bm0YBSVSrky5ePyZMnkzdvXsaMGcPbb78ddEkiIiIiIiKZQkpC6Rwz+xcQY2bXAJOA6ZEtK/upWrUqQ4cOBaB79+58//33AVckIiIiIiISvJSE0seBbcBy4F7gY+CpSBaVXd16663ce++9/PXXX7Rr147M9OyriIiIiIhIEFISSmOAYe7ezt1vBoaFt0ka/Pe//6VOnTqsXbuWu+66S8+XioiIiIjIWS0lofQLjg+hMcDnkSkn+8uTJw+TJk2iYMGCfPDBBwwZMiTokkRERERERAKTklCax90T1jEJv88buZKyvwsvvJDhw4cD8Oijj3L//fczbdo09u3bF3BlIiIiIiIiGSslofSAmdU99sHMLgEORa6ks0Pbtm159NFHOXr0KG+88QY33HADRYsWpXHjxgwaNIhFixYRFxcXdJkiIiIiIiIRZad7ptHMLgXGA7+HN5UCOrj7dxGuLdXMrDXQumLFivesXr066HJOy91ZsGABn376KZ9++ikLFiwgPj4+YX+xYsVo1qwZ7dq1o23btphZgNWKiIiIiIicyMy+c/d6aT4/JRPtmFlOoDJgwM/uHpvWDjNCvXr1fPHixUGXkWq7d+/myy+/TAipGzZsSNj36quv8sADDwRYnYiIiIiIyIkyKpReDpQDoo9tc/f30tpppGXVUJqYu7NmzRrGjRtHv379yJEjBzNnzqR58+ZBlyYiIiIiIpLgTEPpaZ8pNbNRwIvAFcCl4VeaO5SUMTMqVapE3759eeqpp4iPj6d9+/asXLky6NJERERERETSTfTpD6EeUM21oGZgBgwYwMqVK3n//fdp3bo1CxYsoFixYkGXJSIiIiIicsZSMvvuCuDcSBciJ5cjRw5GjhxJ3bp1+fXXX7nppps4cuRI0GWJiIiIiIicsZSE0nOAn8zsUzObduwV6cLkePny5WPatGmUKlWKOXPm8M9//hMNXouIiIiISFaXktt3+0e6CEmZ0qVLM23aNBo1asS7775LtWrV6NmzZ9BliYiIiIiIpFmKZt/NarLD7LunMnHiRDp06ICZMW3aNFq1ahV0SSIiIiIicpbKiNl3G5rZIjPbb2ZHzCzOzPamtUM5c+3bt2fAgAG4O506dWLFihVBlyQiIiIiIpImKXmm9DWgE7AaiAH+Ed4mAerTpw8dO3Zk//79tG7dmq1btwZdkoiIiIiISKqlJJTi7muAKHePc/fhQJOIViWnZWYMGzaM+vXrs379em6++WaOHj0adFkiIiIiIiKpkpJQetDMcgFLzezfZvYwkC/CdUkKxMTE8OGHH3Leeecxd+5cBgwYEHRJIiIiIiIiqZKSUNoZiAIeAA4AZYGbIllUWplZazMbumfPnqBLyTClSpVi7Nix5MiRg0GDBvHll18GXZKIiIiIiEiKafbdbKJfv348/fTTlCpVimXLllG8ePGgSxIRERERkbNAxGbfNbOJ4X+Xm9kPSV9p7VAio0+fPjRq1IgtW7Zwxx13EB8fH3RJIiIiIiIip3Wq23cfCv/bCmidzEsykejoaMaMGUORIkX4+OOPGTJkSNAliYiIiIiInNZJQ6m7bzGzKOBdd9+Q9JWBNUoKlS1bluHDhwPQu3dvzrZbmEVEREREJOs55URH7h5HaPbdQhlUj5yhG264gQceeIDY2Fg6duzI3r17gy5JRERERETkpFIy++5hYLmZvWtmrxx7RbowSbsXXniB2rVr8+uvv3LfffeRHSezEhERERGR7CElofQjoA/wNfBdopdkUnny5GHChAnkzZuXsWPHMnLkyKBLEhERERERSZaWhMnGRowYwZ133knevHn5/vvvqVy5ctAliYiIiIhINhOxJWESdVDJzCab2U9mtvbYK60dSsbp0qULt9xyCwcPHqRDhw4cPnw46JJERERERESOk5Lbd4cDbwJHgabAe8CoSBYl6cPMePPNN7nwwgtZtmwZVatWpUePHnz11VccPXo06PJERERERERSFEpj3P0LQrf6bnD3/sBVkS1L0kvBggWZNGkSpUuXZv369QwZMoSrrrqKEiVK0LlzZyZPnsy+ffuCLlNERERERM5Sp32m1My+ARoBk4Evgc3A8+6eaR9Q1DOlJ4qLi2PBggVMnTqVqVOnsmrVqoR9uXLl4uqrr+a6666jZs2aVK5cmRIlSmBmAVYsIiIiIiJZwZk+U5qSUHopsBIoDDwDFARecPf5ae000hRKT2/VqlUJAXXevHknLBtTsGBBKleuzEUXXcRFF12U8L5KlSrExMQEVLWIiIiIiGQ2EQulZnYzMMPds9zsOAqlqfPnn3/y0Ucf8dVXX/HLL7+watUq9uzZk+yxRYsW5aWXXqJLly4aSRURERERkYiG0inA34BPgHHALHePS2tHGUmh9My4O9u2bUsIqMf+/fHHH1mzZg0A11xzDW+99Rbly5cPuFoREREREQlSRG/fNbOCwI1AR6A2MBUY5+5fp7XDjKBQGhnuznvvvcfDDz/Mrl27yJs3LwMHDqR79+V0CN4AACAASURBVO5ERUUFXZ6IiIiIiAQgouuUuvtedx/p7i2BmsBS4FUz+y2tHUrWZWZ06dKFlStX0r59ew4ePEjPnj3529/+xooVK4IuT0REREREsqCULAmDmRUB2gIdgKLA+5EsKknfFczsXTObnFF9yqmVLFmSCRMmMHXqVM477zwWLFhA3bp16devH3/99VfQ5YmIiIiISBZy0lBqZgXMrLOZfUxo9t1LgYHA+e7eIyWNm9kwM9tqZiuSbL/WzFaZ2Roze/xUbbj7Wne/OyX9Sca6/vrr+emnn+jWrRuxsbE8/fTT1KlTh7lz5wZdmoiIiIiIZBGnGildB1wLvAmUdfeu7v6ln24NmeONCLeRwMyigNeBlkA1oJOZVTOzmmY2I8mrRKquRjJcoUKFePPNN5k9ezaVKlVi5cqVXHnllbRp04aVK1cGXZ6IiIiIiGRypwql57v7re4+3d1j09J4eEKknUk21wfWhEdAjwDjgRvcfbm7t0ry2pqWfiXjNW7cmGXLltGvXz/y5s3L1KlTqVGjBvfeey9btmwJujwREREREcmkThpK3f1ghPosDSSeKGlTeFuyzKyYmf0PqGNmT5ziuK5mttjMFm/bti39qpUUi4mJoX///qxZs4Z7770XM2Po0KFUrFiRPn36sHfv3qBLFBERERGRTCZFEx2lM0tm20lvCXb3He7ezd0vdPfnTnHcUHev5+71ihcvni6FStqUKlWK//3vf6xYsYIbb7yRgwcPMnDgQCpWrMhrr73GkSNHgi5RREREREQyidOGUjNrl5JtqbAJKJvocxng9zNoTzKpKlWq8MEHH/B///d/XH755Wzbto0HH3yQatWq0bdvX7788ksOHToUdJkiIiIiIhIgO928RWb2vbvXPd22U5xfDpjh7jXCn6OBX4Crgc3AIuAWd/8x1dWf2FdroHXFihXvWb169Zk2J+nI3Zk6dSqPP/44q1atStieK1cuGjZsSJMmTWjSpAkNGzYkJiYmwEpFRERERCQ1zOw7d6+X5vNPFkrNrCXwd6A9MCHRroJANXevn4LixgFNgHOAP4F+7v6umf0d+C8QBQxz90FpvYDk1KtXzxcvXpyeTUo6OXr0KDNnzuSrr75i9uzZLF26lMS/g8dCavPmzenRowf58uULsFoRERERETmdSIbS2sDFwNNA30S79gFfufuutHYaaQqlWceuXbuYO3cus2fPPiGkXnTRRYwZM4Z69dL8+y0iIiIiIhEWsVCaqINodz+a1g6CoFCade3atYs5c+bQp08fVqxYQXR0NP379+fxxx8nKioq6PJERERERCSJMw2lJ53oyMwmht8uMbMfkr7S2mEkmVlrMxu6Z8+eoEuRNCpSpAht2rRh0aJF9OjRg6NHj/LUU0/RuHFj1q1bF3R5IiIiIiKSzk51+24pd99iZhckt9/dN0S0sjOgkdLs47PPPqNLly5s2bKFAgUK8Prrr3PbbbdhltzKQiIiIiIiktEiNlIKXACh8JncK60diqTGNddcw/Lly2nbti379u3j9ttvp2PHjuzcuTPo0kREREREJB2cKpS+ceyNmc3LgFpEklWsWDEmT57MsGHDyJ8/PxMnTqRWrVpMnTqV2NjYoMsTEREREZEzcKpQmvj+yDyRLiQ96JnS7MvMuPPOO1m6dCmXXXYZmzdvpk2bNpQoUYLbb7+dDz/8kIMHDwZdpoiIiIiIpNKpnildRmiN0RzAl+H3CUHV3TPt/ZN6pjR7O3r0KEOGDGH48OH8+OOPCdtjYmJo2bIlN954I61ataJw4cIBVikiIiIicnaI5Dql64F4jh8xPcbdvUJaO400hdKzx6pVq5gyZQpTpkxh4cKFCdujo6O5+uqradWqFc2bN6dSpUqaHElEREREJAIivk5pVqRQenb67bff+PDDD5kyZQpz5swhPj4+Yd8FF1xA8+bNad68OVdffTVFihQJsFIRERERkexDoTQZCqWyfft2ZsyYwaeffspnn33Gjh07EvblyJGD+vXr07x5c5o2bUrJkiXJly8f+fPnJ1++fOTKlUujqiIiIiIiKaRQmoiZtQZaV6xY8Z7Vq1cHXY5kEvHx8SxZsoRZs2Yxa9Ysvvnmm1PO2hsdHZ0QUPPnz0/RokWpXLkyVatWpUqVKlSpUoUKFSoQHR2dgVchIiIiIpI5KZQmQyOlcir79+9nzpw5zJo1i/nz57N3717279/PgQMH2L9/f4qWmcmZMyeVKlWiSpUqVK1alfbt21OrVq0MqF5EREREJHOJ5ERHRU91ombflezqyJEjCQH1wIEDbNmyhVWrVvHzzz+zcuVKfv75ZzZu3HjcOXnz5mXhwoVUr149oKpFRERERIIRyVC6DnA0+67ICfbv388vv/zCzz//zOjRo5k5cyaVK1dm0aJFFChQIOjyREREREQyjG7fTYZCqWSkAwcO0KBBA3788Uc6duzI2LFjNVGSiIiIiJw1zjSU5khBB2Zmt5lZn/Dn882sflo7jCQza21mQ/fs2RN0KXIWyZcvH5MnTyZfvnyMHz+eN954I+iSRERERESyjNOGUuAN4DLglvDnfcDrEavoDLj7dHfvWqhQoaBLkbNMlSpVeOeddwB4+OGHWbhwYcAViYiIiIhkDSkJpQ3c/X7gMIC77wJyRbQqkSyoY8eOPPDAA8TGxtKuXbvj1kYVEREREZHkpSSUxppZFKFJjzCz4kB8RKsSyaJefPFF6tevz8aNG+ncuTPx8fpPRURERETkVFISSl8BpgAlzGwQ8H/AsxGtSiSLyp07N5MmTaJo0aLMnDmT5557LuiSREREREQytdOGUncfAzwGPAdsAdq4+6RIFyaSVZ1//vmMGTMGM6Nv37588cUXpzx+9erV/Oc//6F79+5s3749g6oUEREREckcTrVOadFTnejuOyNSUTrQkjCSGfTt25dnnnmGEiVK8P3331O6dGkAYmNj+eabb5gxYwbTp0/nl19+STinWbNmfPLJJ0RFRQVVtoiIiIhIqkRsnVIzW0foOVIDzgd2hd8XBja6e/m0dhopZtYaaF2xYsV7Vq9eHXQ5cpaLi4ujRYsWfPHFF1xxxRXcd999zJgxg5kzZ7J79+6E44oUKULLli357LPP2LZtG/369aN///7BFS4iIiIikgoRC6WJOvgfMM3dPw5/bgk0c/deae000jRSKpnF1q1bqVOnDr///vtx26tUqUKrVq1o3bo1l19+OdHR0Xz++ec0b94cgE8++SThvYiIiIhIZpYRofQ7d78kybbFZ9JppCmUSmYyb948brnlFsqXL0/r1q1p3bo1FStWTPbYAQMG0L9/f8455xyWLFlCmTJlMrhaEREREZHUyYhQ+ikwFxhN6Hbe24Ar3b1FWjuNNIVSyari4uL4+9//zqxZs7j88suZPXs2OXPmDLosEREREZGTOtNQmpIlYToBxQktC/MhUCK8TUTSWVRUFKNHj6Z06dJ8++23PPHEE0GXJCIiIiISUSlZEmanuz8ENAYauftDmXnmXZGsrnjx4kycOJHo6GheeuklpkyZEnRJIiIiIiIRc9pQamY1zWwJsBz40cy+M7MakS9N5Ox1+eWXM3jwYADuuOMOfv311wzp192ZNm0agwcPZv369RnSp4iIiIic3VJy++5bQE93v8DdLwB6AUMjW5aIPPzww9x4443s3buXdu3acfjw4Yj299VXX9GwYUNuuOEGHn/8cSpWrMgdd9zBqlWrItqviIiIiJzdUhJK87n7V8c+uPtsIF/EKhIRAMyMYcOGUaFCBZYsWcJDDz0UkX6+//57WrRowVVXXcXChQspUaIEbdu2BWDkyJFUrVqVDh068MMPP0SkfxERERE5u6Vk9t0pwPfAqPCm24B67t4mwrWlmpm1BlpXrFjxntWrVwddjki6WLJkCZdddhl//fUXL774IjVq1ODAgQPs378/2X9LlSpFnTp1uPjiiylTpgxmlmy7q1evpk+fPkyYMAGAggUL8thjj/HQQw+RP39+1q5dy+DBgxk+fDixsbEAXH/99Tz55JPUr18/w65fRERERDK3jFgSpggwALgCMOBroL+770prp5GmJWEku3n77bfp2rVrqs8rVqwYF198ccKrTp06FChQgGeffZZ33nmHuLg4cufOzYMPPsjjjz9OsWLFTmhj06ZNvPjii7z11lsJtxBfc8019OzZk6uuuopcuXKd8fWJiIiISNYV8VCaFSmUSnbj7vTt25cvvviCfPnykT9//oR/E7+PiYlhw4YNLFmyhCVLlrBz58knys6RIwd33XUXffv2pWzZsqet4c8//+Tll1/m9ddfZ//+/UBodLVly5Zcf/31tGzZkiJFiqTbNYuIiIhI1hCxUGpm0051ortfn9ZOI02hVCQUZDdv3sySJUtYunRpwr8bN26kTZs2DBw4kCpVqqS63Z07d/LGG28wYcIEVqxYkbA9KiqKK6+8khtuuIHWrVtToUKF9LwcEREREcmkIhlKtwG/AeOABYRu3U3g7nPS2mmkKZSKnFx8fDw5cqRkjrPTW7t2LdOnT2fatGnMmTOHuLi4hH01atTgvvvuo2vXrkRHR6dLfyIiIiKS+UQylEYB1wCdgFrAR8A4d/8xrZ1lFIVSkYy3a9cuZs6cybRp05g5cyZ79+4FoGbNmgwZMoSmTZsGXKGIiIiIRMKZhtKTDpe4e5y7f+LuXYCGwBpgtpk9mNbORCT7KlKkCLfccgvjx49n27ZtTJw4kXLlyrF8+XKuuuoqbr75ZtavXx90mSIiIiKSyZzyHj4zy21mbYHRwP3AK8AHGVGYiGRduXLlol27dqxcuZKBAweSN29e3n//fapWrUrfvn05cOBA0CWKiIiISCZxqtt3RwI1gJnAeHdfkeyBmZBu3xXJXDZt2kTv3r0ZO3YsAGXKlOGFF16gQ4cOJ11HNTmHDx/m559/ZsWKFfz444+sWLGCVatW0aBBA958803y588fqUsQERERkZOI5DOl8cCx4YzEBxng7l4wrZ1GmkKpSOb0zTff0L17d77//nsAGjRoQI0aNciZMye5cuVKeCX+vHfv3oQAumbNGuLj45Nt+5JLLuGjjz6iZMmSGXlJIiIiImc9rVOaDIVSkcwrLi6O4cOH869//Ytt27al6tyoqCgqVqxIjRo1qFGjBtWrV6dEiRLcfffd/Prrr5QvX55PPvmEiy66KELVi4iIiEhSCqXJUCgVyfx2797NzJkzOXDgAEeOHOHIkSPExsYmvD/2ypMnD9WrV6d69epUrlyZPHnynNDW1q1bue6661i8eDHFihVjxowZNGzYMICrEhERETn7KJQmQ6FU5Oyzf/9+2rdvz8yZM4mJiWHChAm0bt066LJEREREsr2ILQmTFZlZazMbumfPnqBLEZEMlj9/fqZOncpdd93FoUOHaNOmDW+99VbQZYmIiIjIaWSrUOru0929a6FChYIuRUQCkDNnTt555x369u1LfHw83bp1o2/fvmTHO0JEREREsovooAsQEUlPZsaAAQMoU6YM3bp145lnnmHTpk088sgjmNlJX0WKFKFo0aJBly8iIiJy1tEzpSKSbc2YMYP27dtz6NCh0x4bHR3NSy+9RPfu3dPU144dO3j00UcpV64cvXr1Il++fGlqR0RERCSr0URHyVAoFZFjFixYQK9evdi+fTvuftLX+vXrAXj66ad56qmnMLMU97FhwwZatGjBqlWrAChdujSDBw/mlltuSVU7IiIiIlmRQmkyFEpFJLWGDRvGPffcQ3x8PL169eKFF15IUaD84YcfuPbaa9myZQs1atQgd+7cfPfddwBcdtllDBkyhEsvvTTS5YuIiIgERrPvioikg7vuuovx48eTM2dOXnrpJe69917i4uJOec7s2bNp1KgRW7ZsoXHjxsydO5eFCxcybNgwSpYsybx586hfvz533nknW7ZsyaArEREREclaFEpFRMLatWvH1KlTyZMnD2+//Ta33norsbGxyR47adIkWrRowd69e7n55pv55JNPKFy4MDly5ODOO+/kl19+oXfv3uTKlYsRI0Zw0UUX8fzzz3P48OEMvqoTxcXF8fnnnzNo0CCFZREREQmcbt8VEUni66+/plWrVuzbt4/rrruOSZMmERMTk7D/1Vdf5aGHHsLdeeCBB/jvf/9LVFRUsm2tWbOGRx55hKlTpwJQoUIFOnToQMOGDWnYsCElSpTIkGtyd5YtW8bo0aMZO3ZsQhgtWbIkEydO5Morr8yQOkRERCT70TOlyVAoFZEztXjxYq699lp27NhB48aNmTZtGgUKFODJJ5/kueeeA+C5556jd+/eKXr29LPPPqNHjx789NNPx22vUKECDRs25LLLLqNhw4bUrl2bnDlzptt1/Pbbb4wdO5bRo0ezYsWKhO0XXnghRYsWZdGiRURFRfH888/Tq1cvTcwkIiIiqaZQmgyFUhFJDz/99BPNmjVjy5YtXHrppVSpUoVRo0YRFRXFO++8wx133JGq9o4ePconn3zCt99+y7x581i0aBEHDhw47pg8efJw2WWXcc8993DzzTenKaDu27ePSZMmMWrUKObMmcOx/50vVqwYHTp0oHPnzjRo0IC4uDieeuopBg8eDEDbtm0ZPnw4BQsWTHWfIiIicvZSKE2GQqmIpJe1a9fSrFkz1q1bB0DevHmZPHkyLVu2POO2jx49yooVK5g/fz7z5s1j/vz5/PLLLwn7zzvvPP75z3/StWtXihcvfsq23J358+fzzjvvMGHChISwmzt3bq6//no6d+5MixYtyJUr1wnnfvjhh3Tp0oW9e/dSqVIlPvjgA2rUqHHG1yciIiJnB4XSZCiUikh62rx5M61ateLPP//kww8/pH79+hHra8eOHUyaNIlXXnmFlStXAqFgeeutt9K9e3dq16593PHbtm1j1KhRvPPOOwnHA1xxxRXccccd3HzzzRQqVOi0/a5evZqbbrqJ5cuXkzdvXoYOHcqtt96avhcnIiIi2ZJCaTIUSkUkvbk7cXFxREdHZ1h/n3/+OUOGDOGjjz5K2N64cWMeeughYmJiePfdd5k6dWrCDMElSpSgS5cu3HXXXVSpUiXVfR48eJBu3boxatQoAO6//37+85//JDu6KiIiInKMQmkyFEpFJDtZvXo1r732GsOHD2ffvn3H7cuRIwctW7bk7rvvplWrVmc8SZK789Zbb/HQQw9x5MgR6tWrxzPPPEOLFi00CZKIiIgkS6E0GQqlIpId7d27lxEjRvDWW28RFxfH7bffTpcuXShdunS697Vw4UJuvvlmfvvtNwBq1qzJo48+SseOHdN1dmARERHJ+hRKk6FQKiJy5vbs2cP//vc/hgwZkrCuaZkyZXj44Ye55557KFCgQMAVioiISGZwpqE0R3oWIyIi2UehQoXo3bs369atY9iwYVStWpVNmzbRq1cvypYtyxNPPJEQVkVERETSKtOPlJpZG+A6oATwurvPOt05GikVEUl/8fHxfPzxx/z73/9m7ty5AOTKlYtGjRpRpkwZzjvvPEqVKsV5552X8Dr33HPJnTt3wJWLiIhIJGXq23fNbBjQCtjq7jUSbb8WGAJEAe+4+/MpaKsI8KK73326YxVKRUQia/78+bzwwgtMmTKF0/3/SIkSJejRowe9e/cmRw7doCMiIpLdZPZQeiWwH3jvWCg1syjgF+AaYBOwCOhEKKA+l6SJu9x9a/i8l4Ax7v796fpVKBURyRgbN27kp59+4vfff0/29ccffxAXFwdA27ZtGTlyJPnz509VH/v27aNv375s3bqVZ555hgoVKkTiUkRERCSNMnUoBTCzcsCMRKH0MqC/u7cIf34CwN2TBtJj5xvwPPCZu3+ekj4VSkVEMoe4uDhmzpzJbbfdxp49e6hRowYffvghF154YYrOnzNnDnfccQfr168HIE+ePPzrX//iscce023BIiIimURWnOioNPBbos+bwttO5kGgGXCzmXU72UFm1tXMFpvZ4m3btqVPpSIickaioqJo1aoVCxYsoEqVKqxYsYJLL72Uzz8/9d8YDx06RM+ePWnatCnr16+nTp06dOrUicOHD9O3b19q1ap12jZEREQkawgilCa3+vpJh2vd/RV3v8Tdu7n7/05x3FB3r+fu9YoXL54uhYqISPqoXLky8+fPp1WrVuzatYsWLVrwn//8J9nnURctWkTdunV5+eWXyZEjB/369WPBggWMHTuWL7/8kipVqvDLL79wzTXX0KlTJ80ALCIiksUFEUo3AWUTfS4D/B5AHSIikoEKFSrE1KlTefLJJ4mPj6dXr17cfvvtHDp0CIAjR47Qp08fLrvsMn7++WeqVq3K/Pnz6d+/Pzlz5gSgadOmLFu2jGeffZaYmBjGjx9P5cqVeeWVVzh69GhCX+7O+vXrmTZtGgMHDqRDhw5UrVqVggULct9997F79+5AvgMRERE5URDPlEYTmujoamAzoYmObnH3H9Ohr9ZA64oVK96zevXqM21OREQiZPLkyXTp0oWDBw9Sr149Bg0aRO/evVm6dClmRs+ePXnmmWeIiYk5aRvr1q2je/fuzJgxA4A6derQoEEDfvjhB1asWMHevXtPeu65557LkCFDaNeuHaGpC0RERCStMvVER2Y2DmgCnAP8CfRz93fN7O/AfwnNuDvM3QelZ7+a6EhEJPP74YcfaNOmDevWrUvYVqFCBUaMGEGjRo1S1Ia7M23aNLp3787GjRuP21eyZElq1apFzZo1qVWrFrVq1QLggQce4NtvvwXg73//O6+//jrlypVLUV/z589n/PjxHDhwgAYNGtCwYUOqVatGVFRUCq9aREQk+8nUoTQoCqUiIlnDjh076NChA1988QX33nsvL774YqqXjAE4cOAA7777LnFxcdSsWZOaNWtSsmTJZI+Nj4/n7bffpnfv3uzZs4e8efMyYMAAevToQXR09AnH//rrr4wePZrRo0ezZs2aE/bnz5+f+vXr07BhQxo2bEiDBg0oUaIEALGxsWzevJmNGzeyYcMGNm7cmPA6cuQIffv2pXHjxqm+3ow2depU/vzzT/7xj39orVkRETmBQmkyFEpFRLIOd2fnzp0UK1YsQ/v9448/6NGjBxMmTADg4osvZujQoVx66aXs3LmTiRMnMmrUqIRRVYBSpUpxyy23UKZMGRYsWMD8+fMTlqtJrFy5csTGxvL7778nO5nTMblz52bixIlcf/316X596eHo0aM89thjvPzyywDcdNNNvPfee+TNmzfgykREJDNRKE1Ez5SKiEhqzZw5k/vuu48NGzZgZjRq1Ij58+dz5MgRAPLly0fbtm3p3LkzV1111Qm36v7xxx8JAXX+/PksWrSIAwcOAGBmnHfeeZx//vlccMEFnH/++QnvZ8yYwVtvvUVUVBTDhg3j9ttv/3/t3XlYVdXi//H3AsQpTRxLwaHM0tQcyqF6buUsiUiZU5qZabcwNeXWt7Jrmf1uKSZqZppRKlpappJXM+tiaZldpxQ1w+sAmMN1FhkPZ/3+AM8FPSgoeMA+r+fZz9nDOmuvzbOfBR/23mtf82O/lFOnTtGnTx9WrVqFj48PZcuW5ezZs9xzzz1ER0dz0003ebqJIiJSTCiUuqErpSIiUhDnzp3jjTfe4N133yUzMxMvLy86dOjAgAED6NGjR4FuKXY4HPz++++ULVuWWrVq4evr67actZa///3vjB8/HoCIiAhGjBhRKMdzteLi4ggKCmL37t1UrVqVxYsXU7VqVR5++GH2799P7dq1Wb58OU2aNPF0U0VEpBhQKHVDoVRERK7Ejh072Lx5M+3bt6dmzZrXZJ+TJ09m1KhRALz22mu88cYbhTYisLUWp9NZoIGYVq9eTa9evTh16hRNmjQhOjraNRDU0aNHCQ4O5ueff6ZChQosWrSILl26FEpbRUSk5FIodUOhVERESpI5c+YwePBgMjMzCQ0NZerUqZccUOjo0aMsXLiQzz77jMTERDIyMnA4HBd9ZmZmAlmvy+nevTvdu3enefPmbkOvtZZp06YxatQoMjMzCQ4OZt68eVSoUCFXuZSUFAYNGsTChQvx8vJi6tSphIaGFu4PREREShSF0hz0TKmIiJRUy5Yto3fv3qSlpdG3b1/mzJlDqVKlXNuTk5NZtmwZUVFRrFq1yhU4L8cYk2uwJX9/f4KCgujevTsPPfQQpUuXJj09nWHDhvHhhx8C8OqrrzJu3Lg8g7HT6WTs2LGuW49HjBjBpEmT9GocEZE/KYVSN3SlVERESqKYmBi6d+9OUlISgYGBfPbZZ/z8889ERUXx5ZdfkpSUBICPjw9dunShf//+tG7dGl9fX3x8fChVqlSuT29vb9LS0oiJiSE6Opro6Gj++OMP1/5uuOEGOnfuzOHDh/nxxx8pU6YMkZGR9O3bN1/tnTt3Lk8//TQZGRk8/PDDLFiwgIoVKxbJz0ZERIovhVI3FEpFRKSk2rhxI126dOH48eP4+vq6RgEGaNu2LY8//ji9evWiWrVqBa7bWsvmzZtdAXXr1q2ubTVr1mTp0qXcc889Barzhx9+ICQkhBMnTuDt7c0dd9xB8+bNXVOzZs3w8/MrcFtFRKTkUCh1Q6FURERKst9++42OHTuSmJjIbbfdRv/+/enXrx/169cv1P3Ex8fz1VdfERcXx4svvnjFgzvFxcUxcOBANmzYgNPpvGh7nTp1aN68OS1atCA4OJimTZtebdNFRKQYUSh1Q6FURERKupMnT5KYmEjjxo0LbTTeopacnMz27dvZsmULW7duZcuWLWzbto3U1NRc5Zo2bcqAAQPo16/fNRvlWEREio5CaQ4a6EhERKR4Of/e1i1btrB27Vo+//xzTpw4AZDrfbAhISGUL1/ew60VEZEroVDqhq6UioiIFE/p6emsWLGCuXPnsnz5cjIyMgAoX748jz76KMHBwZQrVw5jpbSQ7wAAGrZJREFUDF5eXhhjck1eXl44nU4yMzNxOBxuJ6fTSdOmTbnrrrtKzFVmEZGSTKHUDYVSERGR4u/48eMsWrSIefPmsX79+kKvv169eoSEhBASEkLbtm31yhoRkSKiUOqGQqmIiEjJEhcXR1RUFL/88gtOpxNrrevzwglwvfbG3eRwOIiJieHo0aOu+qtXr05wcDAhISG0a9eO0qVLF/kxJScns2DBAlJTU6lUqRJ+fn4XTdeiHSIiRU2h1A2FUhERkT+3zMxM1q9fz5IlS1iyZAn79u1zbatQoQKBgYF069aNzp07X9HrdS7n0KFDBAcH8+9///uS5cqUKYO/vz/Dhw/nmWeewdfXt9DbIiJS1BRKc9BARyIiInIhay3btm1zBdRt27a5thljaNWqFYGBgQQGBtKiRQu8vLyuan/btm2jW7duJCQkULduXbp27crJkydd06lTp1zzDofD9b169eoxfvx4+vTpc9VtEBG5lhRK3dCVUhEREcnL3r17iY6OZuXKlaxZs4b09HTXturVq9O1a1cCAwPp1KkTlSpVKlDdK1asoHfv3iQlJdG2bVuWLl1K9erV3Za11nLu3Dm+/fZbXnnlFXbt2gVAs2bN+Mc//kHnzp0LZaAmay1ffPEFM2fOZPjw4XTv3v2q6xQRyUmh1A2FUhEREcmPpKQkYmJiWLFiBStWrCA+Pt61rXTp0jz55JOEhYVRv379y9Y1bdo0Ro4cidPppG/fvkRGRlKmTJl8tcPhcDBnzhzGjh3LwYMHAXjooYd4++23adWq1ZUdHPDHH38QGhrK0qVLgawrw9OmTSM0NPSK6xQRudDVhlLdGyIiIiJ/WjfccANBQUHMmDGD/fv3Exsby4QJE3jggQdIS0tj5syZNGjQgMcee4y8/uHtcDgYNmwYw4cPx+l0MnbsWObPn5/vQArg4+PD4MGDiYuLY8KECVSqVImYmBhat25Nz549XVdR88tay0cffUSjRo1YunQpFSpU4PHHH8day7Bhw3j55Zcp6IWJw4cPM3DgQHr37s3atWsL/H0RkTy5G9WupE8tW7a0IiIiIldj586ddtCgQbZUqVIWsIBt166dXbVqlXU6ndZaa0+fPm27dOliAevr62ujoqIKZd8nTpywL730ki1Tpoxr361bt7ZTpkyxhw4duuR39+7da9u3b+/63sMPP2wTEhKstdZ+/PHH1tvb2wJ2wIABNi0t7bJtcTqddu7cudbPz89VJ2Bbtmxp58+fb9PT0wvlmEWk5AI22qvIb7p9V0REROQSDh48SEREBDNnzuTs2bNA1nOfoaGhTJkyhdjYWKpWrcqSJUu4//77C3XfiYmJvPnmm8yfP59z584B4OXlRYcOHejXrx8hISFUrFgRyBpx+L333uOVV14hOTmZKlWqMHXqVPr27Zvr2dSvv/6anj17cu7cOTp06MDixYtddbg79r/+9a8sX74cgM6dO3PPPffwwQcfcOzYMQBq1arF888/z9ChQ/Hz8yvU4xeRkkHPlLqhUCoiIiKF7dSpU3zwwQdERERw5MgR1/o77riD5cuXc+uttxbZvs+dO8dXX33FggULWLlypWvU3tKlSxMUFERQUBAffPAB69evB6BPnz5MmTIlz0GWNm3aRGBgIEePHqVZs2asWLGCm2++2bXdWktkZCSjRo3izJkz3HjjjURERDBw4ECMMaSkpBAVFcXkyZNdtxaXK1eOQYMGMWLECG677bYi+1nIpWVkZFCqVClPN0P+ZBRKc9ArYURERKSopaamMnfuXN577z3q1avHnDlzCjxK79U4fvw4ixcvZsGCBXz//fe5ttWsWZMZM2bka4TdvXv30qVLF+Li4qhTpw4rV66kYcOGHDhwgCFDhrB69WoAV+CtWbPmRXVYa1m1ahWTJ0/mm2++AbIGUxo4cCCTJ0++pj8XgVWrVtG7d2+6devG3Llz9WohuWYUSt3QlVIRERH5M0hISGDhwoX885//pEmTJowbN65AQfDYsWN069aNDRs24OfnR2hoKBERESQlJVG5cmWmTZt20e2/eYmNjSUiIoJ58+aRnp5OrVq1+PDDD+natevVHKLk0y+//EK7du1ct3mHhYUxceJED7dK/iwUSt1QKBURERHJn+TkZPr27Ut0dLRr3aOPPsr06dOpUaNGgevbvXs3gwYNct1KPHjwYCZNmsSNN9542e9aa/nXv/7F1KlT2b9/Px06dCAoKIj7778fHx+fArflz+K3337j/vvv5/jx47Rv357vv/8eh8PBzJkzGTp0qKebJ38CCqVuKJSKiIiI5J/D4eBvf/sbX3/9NW+++SY9e/a8qvoyMzOZPHkyY8aMIS0tDX9/fz766CM6derktnxKSgoLFiwgIiKC2NjYi7b7+fkRGBhIUFAQXbp0yVfA/bNITEzkvvvuIz4+nsDAQJYuXcq8efMYPHgw3t7erFixIs+fu0hhUSh1Q6FURERExPN27drFk08+yS+//ALA0KFDCQ8Pp0KFCgAcOnSI999/P9dovjfffDPPPfccbdu2ZdWqVURHR7N7925XnT4+PjzwwAN0796de++9l4CAAKpVq/anfH7yxIkT/OUvf2HHjh20adOGb7/9lvLlywPw8ssv8/bbb1OxYkV+/PFHGjdu7OHWyvVModQNhVIRERGR4sHhcBAeHs7YsWNJT0+nTp06jBs3jtWrV7Nw4UIyMjIAaNGiBS+88AK9evXC19c3Vx2///47X331FdHR0axbtw6n05lre6lSpahVqxb+/v4EBATg7++Pv78/tWvXpmPHjq6gdj1JTk6mY8eO/PTTTzRs2JC1a9dSpUoV13an00mfPn34/PPPqVOnDhs2bLii27FF8kOh1A2FUhEREZHiZceOHQwcOJBNmza51nl5eRESEsLIkSO577778jWg0vHjx1m5ciXLly/nt99+IzExkePHj+dZ/pZbbiEqKoq2bdsWynEUBxkZGTzyyCMsX74cf39/fvrpJwICAi4ql5KSwkMPPcSGDRto1aoVMTExlCtXzgMtluudQqkbCqUiIiIixU9GRgYTJkzgk08+ITg4mGHDhlG3bt2rrjc5OZmDBw+SmJiYa1qzZg07d+7E29ubMWPGMGbMmBI/YJK1lqeeeopPPvmEypUrs27dOho2bJhn+SNHjtC6dWsOHDjAo48+yqJFi67Jrc5Lly5lyJAhPPjgg7zzzjvccsstRb5P8RyFUjcUSkVEREQkLS2N1157jfDwcKy1tG7dmqioKOrXr+/ppl2xl156iQkTJlCuXDm+++472rRpc9nv7Nixg3vvvZczZ87w0ksv8fbbbxdpG5cuXcpjjz2Gw+EAwNfXlxEjRvDqq69qkKrrlEJpDsaYICCofv36Q+Li4jzdHBEREREpBmJiYnjiiSdITEykfPnyTJ06lUGDBuXrduG8pKens2PHDjZv3szWrVtJSkrC29sbLy8vvL29XdP55bJly9KjRw9atmx5RftLS0vjnXfeYezYsfj4+BAdHV2gd8CuXr2arl27kpmZyezZsxk8ePAVteNycgbS559/ntOnTzN37lwAqlWrxrhx43j66adL/BVryU2h1A1dKRURERGRnE6ePMmzzz7LwoULAXjkkUeYNWtWrsGB8pKamsq2bdvYvHmza9q+fTvp6ekFbseDDz5IWFgYXbt2zddttMePH2fmzJlMmzaNw4cPAzBv3jz69+9f4H3PmjWLZ555Bm9vb2655RbKlCmT51SvXj1GjhyJn59fvutftmwZPXv2dL1i6J133sEYw8aNG3nhhRdYt24dAHfeeSeTJk2ic+fOBT4GKZ4USt1QKBURERGRC1lriYqKIjQ0lLNnz3LzzTczffp0qlSpwpEjR1zT0aNHcy3Hx8eTmZl5UX0NGjSgRYsWtGjRgipVquB0OsnMzHQ7JSQkMGfOHM6ePQvAHXfcwejRo+nfvz9lypS5qO49e/YwefJkPvnkE5KTkwFo0qQJr7/+Oo888sgV/wzGjBnDW2+9la+y1atXJzw8nP79+1/2qnLOQBoWFsaECRNyfcday+LFi3nxxRfZt28fAF27dmXixIk0atToqq5au5OSksKuXbuIjY0lNjaWQ4cOMWDAgCJ7Z2t6ejrLly/nyy+/pHv37vTq1atI9lNcKZS6oVAqIiIiInnZt28fAwYM4Mcff8xXeS8vLxo2bOgKoC1btuSuu+6iYsWKBdrv6dOnmT17NhERESQmJgJZwW/YsGE8++yzVKlShXXr1vHuu++ybNkyzv+d3rlzZ0aPHk2HDh0KJbwdPnyY06dPk5qa6nZKSUkhMjKStWvXAvDAAw/w/vvv06hRI7f1LVu2jMcee4yMjAy3gTSn1NRUpk6dyvjx410B/YYbbqB27doEBARc9BkQEICfnx+ZmZk4HA63U3p6Ovv27XMF0NjYWP7zn/9c9OoggEGDBjFp0qQCXQG+lO3bt/Pxxx8zb94817t2AaZMmcLw4cMLZR8lgUKpGwqlIiIiInIpDoeDiRMnsmDBAipWrEiNGjWoUaMG1atXd82fn2rVqlWor1LJyMhg0aJFhIeHs3XrVgDKli1L/fr12b59O5A1OFD//v154YUXaNy4caHtO7+stcydO5ewsDCOHTuGj48PYWFhvPbaa7l+FtHR0fTs2ZOMjAxGjx7NxIkT8xWcjx49ytixY4mKiiIpKanQ2+/t7c3tt99O48aNady4sWvk57S0NG666SZmzJhBjx49rqjuU6dO8emnnxIZGUnOzNG4cWPatGnD7NmzAXj99df5+9//XuhXgYsjhVI3FEpFREREpLiz1hITE0N4eDgrV64EoEqVKjz33HOEhoZSo0YND7cQTpw4wSuvvMKsWbOw1lKnTh2mTZtGUFDQFQfSnKy1nDx5koSEBOLj40lISMg1Hx8fz5kzZyhVqhQ+Pj6uydvbO9eyv7+/K4A2adKEBg0aULp06Vz72r17N4MHD3ZdIe/duzfTpk2jWrVql21ncnIya9asYf78+Xz55ZekpqYCcOONN9KvXz+eeuopWrZsiTGGyMhIhgwZgtPpZMSIEbz77rvX5DU8nqRQ6oZCqYiIiIiUJDt37mTPnj106NChUK/KFpaff/6ZZ5991nVlt127dqxdu5aMjAxGjRpFeHh4ibgi6HQ6mT59Oi+//DLnzp2jSpUqTJ06lb59++Zqv9Pp5Ndff+Wbb75h9erVrF27NtfAVu3bt+epp54iJCSEsmXLXrSfxYsX069fP9LT0xk4cCCzZ8++rkccVih1Q6FURERERKRwORwOpk+fzmuvveZ6HrQkBdKc9u3bx5AhQ/juu+8ACAoKYty4cbmC6H//+19XeWMMd999N926deOJJ56gbt26l93H6tWr6dGjB8nJyfTo0YNPP/3U7aBWBXHmzBkSEhI4ePAgDRo0yFc7rgWFUjcUSkVEREREisYff/zBW2+9Rd26dQkLCytxgfQ8ay2RkZGMHj2a06dPX7Q9ICCATp060alTJ9q3b5+v1wddaP369QQGBnLq1Cnat2/PkiVLqFChQp7lU1JS2LZtG7t27XLdypxzOnPmjKusj48PoaGhjB07ttAGbrpSCqVuKJSKiIiIiEh+HDx4kOHDh/PDDz/QunVrVxC9/fbbCyVwb9u2jU6dOnHkyBFatWrFypUrqVy5suv9t5s2bWLjxo1s2rSJ2NhYt68fOq9s2bIEBARQrVo1fvrpJ6y1VK5cmXHjxvHMM8947BZhhVI3FEpFRERERKS42LNnDx07dmT//v3ceuutVKhQgdjYWBwOR65y518/1LRpU+rUqeN6Lc75qXLlyq6g/OuvvzJy5EjWrFkDwJ133snkyZPp2LHjtT48hVJ3FEpFRERERKQ4OXjwIJ06dWLnzp3A/wJoy5YtadmyJXfffTd33XUX5cuXz3ed1lqWLFlCWFgY+/btA7Kejw0PD6dBgwZX3WaHw4HT6cTX1/eS5RRK3VAoFRERERGR4ub06dN888031KxZk2bNmhUogF5KamoqU6ZMYfz48SQlJVGqVCmef/552rVrR9myZXNN5cqVc80DJCQkcODAAQ4cOEB8fLxr/sCBAxw8eJDMzEyqV69OQEAA/v7+rinncv369RVKzzPGBAFB9evXHxIXF+fp5oiIiIiIiFwzhw8f5tVXX+Xjjz+msHKet7f3JZ9zzaZQeiFdKRURERERkT+rzZs3ExERwbFjx0hJSSE5OZmUlJSLJqfTSa1atahTp06uqXbt2q5nWn18fDhy5AgJCQkkJiaSmJh40Xx8fLxC6YUUSkVERERERK6Nq32m1KswGyMiIiIiIiJSEAqlIiIiIiIi4jEKpSIiIiIiIuIxCqUiIiIiIiLiMQqlIiIiIiIi4jEKpSIiIiIiIuIxCqUiIiIiIiLiMQqlIiIiIiIi4jEKpSIiIiIiIuIxCqUiIiIiIiLiMQqlIiIiIiIi4jEKpSIiIiIiIuIxCqUiIiIiIiLiMQqlIiIiIiIi4jEKpSIiIiIiIuIxxT6UGmMaGmM+MMZ8YYx51tPtERERERERkcJTpKHUGBNpjDlqjIm9YH0XY8xuY8weY8z/XaoOa+0ua+1fgV7A3UXZXhEREREREbm2ivpK6SdAl5wrjDHewHSgK9AI6GuMaWSMaWKMWX7BVD37O92BdcB3RdxeERERERERuYZ8irJya+0Pxpi6F6xuBeyx1u4FMMZ8BgRba/8BdMujnmgg2hjzT2BB0bVYRERERERErqUiDaV5qAUk5FhOBFrnVdgY8yDwCFAaWHGJckOBodmLaRfeMixSzFUFjnm6ESL5pPNVShqds1LS6JyVkub2q/myJ0KpcbPO5lXYWrsGWHO5Sq21s4BZAMaYjdZaPX8qJYbOWSlJdL5KSaNzVkoanbNS0hhjNl7N9z0x+m4iEJBj2R/4wwPtEBEREREREQ/zRCj9N3CbMaaeMcYX6ANEe6AdIiIiIiIi4mFF/UqYT4H1wO3GmERjzGBrrQMYBqwCdgGLrLU7CnnXswq5PpGipnNWShKdr1LS6JyVkkbnrJQ0V3XOGmvzfJxTREREREREpEh54vZdEREREREREeA6C6XGmC7GmN3GmD3GmP/zdHtELmSMCTDGxBhjdhljdhhjRmSvr2yMWW2Micv+9PN0W0VyMsZ4G2O2GGOWZy/XM8ZsyD5nF2aPESBSLBhjKhljvjDG/Jbd37ZVPyvFlTHmhey/CWKNMZ8aY8qoj5XixhgTaYw5mvO1m3n1qybL1OxMts0Y0+Jy9V83odQY4w1MB7oCjYC+xphGnm2VyEUcwGhrbUOgDRCafZ7+H/CdtfY24LvsZZHiZARZ4wCc9w4wOfucPQkM9kirRNybAnxtrb0DuIusc1f9rBQ7xphawHDgbmttY8CbrEFA1cdKcfMJ0OWCdXn1q12B27KnocCMy1V+3YRSoBWwx1q711qbDnwGBHu4TSK5WGsPWWs3Z8+fJesPpVpknatzsovNAXp4poUiFzPG+AMPA7Ozlw3QDvgiu4jOWSk2jDEVgb8AHwFYa9OttadQPyvFlw9Q1hjjA5QDDqE+VooZa+0PwIkLVufVrwYDc22Wn4FKxpibL1X/9RRKawEJOZYTs9eJFEvGmLpAc2ADUMNaewiygitQ3XMtE7lIBPAi4MxergKcyh5NHdTfSvFyC/Bf4OPsW85nG2PKo35WiiFr7UEgHIgnK4yeBjahPlZKhrz61QLnsusplBo36zS0sBRLxpgbgMXASGvtGU+3RyQvxphuwFFr7aacq90UVX8rxYUP0AKYYa1tDpxDt+pKMZX9DF4wUA+oCZQn69bHC6mPlZKkwH8nXE+hNBEIyLHsD/zhobaI5MkYU4qsQDrfWvtl9uoj529ryP486qn2iVzgPqC7MWY/WY9FtCPrymml7FvNQP2tFC+JQKK1dkP28hdkhVT1s1IcdQD2WWv/a63NAL4E7kV9rJQMefWrBc5l11Mo/TdwW/ZoZb5kPSQe7eE2ieSS/SzeR8Aua+27OTZFAwOz5wcCy65120Tcsda+bK31t9bWJatf/Ze19nEgBuiZXUznrBQb1trDQIIx5vbsVe2BnaifleIpHmhjjCmX/TfC+fNVfayUBHn1q9HAE9mj8LYBTp+/zTcvxtrr524AY0wgWf/B9wYirbVvebhJIrkYY+4H1gLb+d/zea+Q9VzpIqA2Wb+gHrPWXvgwuYhHGWMeBMKstd2MMbeQdeW0MrAF6G+tTfNk+0TOM8Y0I2tgLl9gLzCIrH/Eq5+VYscY8wbQm6wR+rcAT5P1/J36WCk2jDGfAg8CVYEjwFhgKW761ex/sLxH1mi9ycAga+3GS9Z/PYVSERERERERKVmup9t3RUREREREpIRRKBURERERERGPUSgVERERERERj1EoFREREREREY9RKBURERERERGPUSgVERG5CsaYpCKoc78xpqon9i0iInKtKZSKiIiIiIiIx/h4ugEiIiLXG2NMEDAG8AWOA49ba48YY14H6gE3Aw2AUUAboCtwEAiy1mZkV/M3Y8xD2fP9rLV7jDH1gAVk/f7+Osf+bgCWAX5AKWCMtXZZ0R6liIhI4dCVUhERkcK3DmhjrW0OfAa8mGPbrcDDQDAQBcRYa5sAKdnrzztjrW0FvAdEZK+bAsyw1t4DHM5RNhUIsda2AB4CJhljTOEfloiISOFTKBURESl8/sAqY8x24G/AnTm2rcy+Grod8OZ/Vzy3A3VzlPs0x2fb7Pn7cqyfl6OsAf6fMWYb8C1QC6hRKEciIiJSxBRKRURECt804L3sK6DPAGVybEsDsNY6gQxrrc1e7yT3YzU2H/PnPQ5UA1paa5sBRy7Yp4iISLGlUCoiIlL4biTrGVGAgVdYR+8cn+uz538E+mTPP37B/o5aazOyn0Otc4X7FBERueY00JGIiMjVKWeMScyx/C7wOvC5MeYg8DNZgxsVVGljzAay/oHcN3vdCGCBMWYEsDhH2fnAV8aYjcBW4Lcr2J+IiIhHmP/dNSQiIiIiIiJyben2XREREREREfEYhVIRERERERHxGIVSERERERER8RiFUhEREREREfEYhVIRERERERHxGIVSERERERER8RiFUhEREREREfEYhVIRERERERHxmP8Pxiek8gBnx6AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
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    }
   ],
   "source": [
    "plt.subplot(111)\n",
    "plt.plot(lamd_mat, variance_coef,  color='black', linewidth = 2, label = 'Slope Variance')\n",
    "plt.title('Model Fit Variance vs. Lambda'); plt.xlabel('Lambda'); plt.ylabel('Model Fit Variance')\n",
    "plt.xlim(0.,100.); plt.ylim(0.001,10.0); plt.yscale('log')\n",
    "plt.subplots_adjust(left=0.0, bottom=0.0, right=2.0, top=1.0, wspace=0.2, hspace=0.2)\n",
    "plt.legend()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is as expected, with increase in lambda hyperparameter the sensitivity of the model to the training data is decreased.\n",
    "\n",
    "#### k-fold Cross Validation\n",
    "\n",
    "It would be useful to conduct a complete k-fold validation to evaluate the testing error vs. the hyperparameter lambda for model tuning.\n",
    "\n",
    "* the following code should do this \n",
    "\n",
    "* but with a single feature as input for fitting the fit function requires a reshape\n",
    "\n",
    "```python\n",
    "my_array.reshape((nsample,1))\n",
    "```\n",
    "\n",
    "* this is not included in the scikit learn function 'cross_val_score' so we will skip this for now\n",
    "\n",
    "I have left the code commented out below for reference:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "#score = []                                                  # code modified from StackOverFlow by Dimosthenis\n",
    "#nlambda = 1\n",
    "#lambd_mat = np.linspace(0.0,100.0,nlambda)\n",
    "#for ilam in range(0,nlambda):\n",
    "#    ridge_reg = Ridge(alpha=lambd_mat[ilam])\n",
    "#    scores = cross_val_score(estimator=ridge_reg, X= df['Density'].values, y=df['Porosity'].values, cv=10, n_jobs=4, scoring = \"neg_mean_squared_error\") # Perform 10-fold cross validation\n",
    "#    score.append(abs(scores.mean()))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Comments\n",
    "\n",
    "Ridge regression is a variant of linear regression that includes a hyperparameter to constrain the degree of model fit.  This allow us to tune the variance-bias trade-off of our model. I hope this was helpful,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "On twitter I'm the @GeostatsGuy.\n",
    "\n",
    "\n",
    "***\n",
    "\n",
    "#### More on Michael Pyrcz and the Texas Center for Geostatistics:\n",
    "\n",
    "### Michael Pyrcz, Associate Professor, University of Texas at Austin \n",
    "*Novel Data Analytics, Geostatistics and Machine Learning Subsurface Solutions*\n",
    "\n",
    "With over 17 years of experience in subsurface consulting, research and development, Michael has returned to academia driven by his passion for teaching and enthusiasm for enhancing engineers' and geoscientists' impact in subsurface resource development. \n",
    "\n",
    "For more about Michael check out these links:\n",
    "\n",
    "#### [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n",
    "\n",
    "#### Want to Work Together?\n",
    "\n",
    "I hope this content is helpful to those that want to learn more about subsurface modeling, data analytics and machine learning. Students and working professionals are welcome to participate.\n",
    "\n",
    "* Want to invite me to visit your company for training, mentoring, project review, workflow design and / or consulting? I'd be happy to drop by and work with you! \n",
    "\n",
    "* Interested in partnering, supporting my graduate student research or my Subsurface Data Analytics and Machine Learning consortium (co-PIs including Profs. Foster, Torres-Verdin and van Oort)? My research combines data analytics, stochastic modeling and machine learning theory with practice to develop novel methods and workflows to add value. We are solving challenging subsurface problems!\n",
    "\n",
    "* I can be reached at mpyrcz@austin.utexas.edu.\n",
    "\n",
    "I'm always happy to discuss,\n",
    "\n",
    "*Michael*\n",
    "\n",
    "Michael Pyrcz, Ph.D., P.Eng. Associate Professor The Hildebrand Department of Petroleum and Geosystems Engineering, Bureau of Economic Geology, The Jackson School of Geosciences, The University of Texas at Austin\n",
    "\n",
    "#### More Resources Available at: [Twitter](https://twitter.com/geostatsguy) | [GitHub](https://github.com/GeostatsGuy) | [Website](http://michaelpyrcz.com) | [GoogleScholar](https://scholar.google.com/citations?user=QVZ20eQAAAAJ&hl=en&oi=ao) | [Book](https://www.amazon.com/Geostatistical-Reservoir-Modeling-Michael-Pyrcz/dp/0199731446) | [YouTube](https://www.youtube.com/channel/UCLqEr-xV-ceHdXXXrTId5ig)  | [LinkedIn](https://www.linkedin.com/in/michael-pyrcz-61a648a1)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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